Document Classification for Large Datasets Based …interval-valued intuitionistic fuzzy sets[18]. F. Herrera, et.al. “A fusion approach for managing multi-granularity linguistic

Advances in Fuzzy Mathematics.

ISSN 0973-533X Volume 12, Number 3 (2017), pp. 677-692

© Research India Publications

http://www.ripublication.com

Document Classification for Large Datasets Based On

Hesitant Fuzzy Linguistic Term Set

Swatantra Kumar Sahu 1, Bharat Mishra2 and R. S. Thakur3

1 M.G.C.G.V.V., Satna, Madhya Pradesh, India.

2 M.G.C.G.V.V., Satna, Madhya Pradesh, India. 3 MANIT, Bhopal, Madhya Pradesh, India.

Abstract

This paper presents Hesitant Fuzzy information about large data sets. Hesitant

Fuzzy Linguistic Term Set (HFLTS) is based on the fuzzy linguistic approach

that will serve as basis to Increase the flexibility of elicitation of linguistic

Information. Experimental results evaluated using the Analytical Tool

MATLAB 7.14. The classification results show the proposed approach

performs well.

Keywords: Hesitant Fuzzy Set, Classification, Large Data sets, Linguistic

Term Set.

1. INTRODUCTION

Hesitant Fuzzy Information collection is refer Fuzzy logic, Fuzzy sets theory,

Intuitionistic fuzzy sets, Fuzzy multi sets, fuzzy linguistic approach, uncertainty and

loading of data etc. In this Paper Hesitant Fuzzy Linguistic Term Set (HFLTS) is used

to classify the document datasets.

Fig 1: Hesitant Fuzzy Information collection

Hesitant Fuzzy set

Linguistic Term Set Dual S et

678 Swatantra Kumar Sahu, Bharat Mishra and R.S. Thakur

In the area of document classification various approach proposed by researcher some

of listed blow Swatantra Kumar Sahu, et.al.“Hesitant Fuzzy Linguistic Term Set

Based Document Classification”[48], S.A. Orlovsky, “Decision-making with a fuzzy

preference relation[25], Swatantra Kumar Sahu, et.al “Numerical Result Analysis of

Document Classification for Large Data Sets” [49],H. Becker, “Computing with

words and machine learning in medical diagnosis[2],Y.Dong,et.al.“Computing the

numerical scale of the linguistic term set for the 2-tuple fuzzy linguistic representation

model [5].

L. Martinez, et.al. “Computing with words in decision support systems: An overview

on models and applications [21], D.Dubois, et.al. Fuzzy Sets and Systems: Theory

and Applications [6]. Z. P. Fan, et.al. “An approach to multiple attribute decision

making based on fuzzy preference information alternatives [7], D. F. Li,“TOPSIS-

based nonlinear-programming methodology for multi attribute decision making with

interval-valued intuitionistic fuzzy sets[18].

F. Herrera, et.al. “A fusion approach for managing multi-granularity linguistic terms

sets in decision making[10], F. Herrera et.al. “A 2-tuple fuzzy linguistic

representation model for computing with words[12]S. Kundu, “Min-transitivity of

fuzzy leftness relationship and its application to decision making [16], H. Ishibuchi

et.al. “Theory and methodology: Multi objective programming in optimization of the

interval objective function [14].

G. Bordogna et.al. “A fuzzy linguistic approach generalizing Boolean information

retrieval: A model and its evaluation [4], J. Kacprzyk et.al. “Computing with words is

an implementable paradigm: Fuzzy queries, linguistic data summaries, and natural-

language generation[15].

H. Ishibuchi, et.al. , Classification and Modelling With Linguistic Information

Granules: Advanced Approaches to Linguistic Data Mining [13],D. F. Li, “Multi

attribute group decision making method using extended linguistic variables[17].

P. P. Bonissone, “A fuzzy sets based linguistic approach: Theory and applications

[3],J. Ma, et.al., “A fuzzy-set approach to treat determinacy and consistency of

linguistic terms in multi-criteria decision making[19], F. Herrera, E. Herrera-Viedma,

et.al., “A fuzzy linguistic methodology to deal with unbalanced linguistic term

sets[11], L. Mart´ınez, “Sensory evaluation based on linguistic decision analysis[20].

J. M. Mendel, “An architecture for making judgement using computing with

words[22],K.T. Atanassov, “Intuitionistic fuzzy sets[1], J.M. Mendel, et.al.,“What

computing with words means to me[23], M. Mizumoto et.al., “Some properties of

fuzzy sets of type 2[24], Rosa M. Rodr´ıguez, et.al., “Hesitant Fuzzy Linguistic Term

Sets for Decision Making”[44].J.M. Garibaldi, et.al., “Nonstationary fuzzy sets [8].

W. Pedrycz et.al., “Analytic hierarchy process (AHP) in group decision making and

its optimization with an allocation of information granularity [27], F. Herrera, et.al.,

“Computing with words in decision making: Foundations, trends and prospects[9] ,

M. Roubens, “Some properties of choice functions based on valued binary

Document Classification for Large Datasets Based On Hesitant Fuzzy… 679

relations[28].

V.Torra, “Negation function based semantics for ordered linguistic labels[31], R. R.

Yager, “On the theory of bags[37],V. Torra, “Hesitant fuzzy sets[32], Y. Tang et.al.

“Linguistic modelling based on semantic similarity relation among linguistic

labels[30], I. B. T¨urks¸en, “Type 2 representation and reasoning for CWW[33].

Y. M.Wang, J et.al., “A preference aggregation method through the estimation of

utility intervals [35], L. A. Zadeh, “The concept of a linguistic variable and its

applications to approximate reasoning—Part I[40].

D.Wu et.al., “Computing with words for hierarchical decision making applied to

evaluating a weapon system [36], A. Sengupta et.al., “On comparing interval numbers

[29].

R. R. Yager, “An approach to ordinal decision making [38], J. H. Wang et.al., “A new

version of 2-tuple fuzzy linguistic representation model for computing with words

[34], L. A. Zadeh, “The concept of a linguistic variable and its applications to

approximate reasoning—Part II[41] L. A. Zadeh, “Fuzzy sets[39]. L. A. Zadeh, “The

concept of a linguistic variable and its applications to approximate reasoning—Part

III[42].

S. M. Zhou, R et.al., “On aggregating uncertain information by type-2 OWA

operators for soft decision-making[43],S. Parsons, “Current approaches to handling

imperfect information in data and knowledge bases[26],Hesitant Distance Similarity

Measures for Document Clustering[45].

Hesitant k-Nearest Neighbor (HK-nn) Classifier for Document Classification and

Numerical Result Analysis[47], Computing Vectors Based Document Clustering and

Numerical Result Analysis[46].

This paper is organized as follows. Section-1 described the introduction and review of

literatures. In Section-2, the Hesitant Fuzzy Information is described. In Section-3,

Methodology of document Classification is described. In Section-4, Experimental

results are described. Finally, we concluded and proposed some future directions in

Conclusion Section, i.e. Section 5.

2 HESITANT FUZZY LINGUISTIC TERM SET

Uncertainty problem is occurs during calculation of document classification results,

for handling this problem the best and optimum solution is Hesitant Fuzzy Set.

Hesitant Fuzzy Set gives new computational solution with numerical capability.

Hesitant Fuzzy used Linguistic Term Set it knows Hesitant Fuzzy Linguistic Term Set

(HFLTS). Linguistic Term Set just like Context Free Grammar (CFG) [44].

Definition 1: Let S be a linguistic term set, S={S0,-----,Sg}, an HFLTS, Hs, is an

ordered finite subset of the consecutive linguistic terms of S. and define the empty

HFLTS and the full HFLTS for a linguistic variable λ as follows.

680 Swatantra Kumar Sahu, Bharat Mishra and R.S. Thakur

1) Empty HFLTS: Hs(λ)={}

2) Full HFLTS: Hs(λ)=S.

Any other HFLTS is formed with at least one linguistic term in S.

Example 1: Let S be a linguistic term set S={ S0:nothing, S1:verylow,S2:low,S3 :

medium, S4:high,S5:veryhigh,S6:perfect} a different HFLTS might be

Hs(λ)={ S1 :very low, S2 :low, S3 : medium }

Hs(λ)={ S3 :medium, S4: high, S5:veryhigh, S6:perfect }

Once the concept of HFLTS has been defined, it is necessary to introduce the

computation and operations that can be performed on them.

Let S be a linguistic term set, S= {S0,-----,Sg},and Hs , Hs1 ,Hs2 be the three HFLTS.

Definition 2: The upper bound Hs+ and lower bound Hs- of the HFLTS, Hs are

defined as

1) Hs+ =max(si )=sj , si Hs, si ≤ sj for all i

2) Hs- =min(si )=sj , si Hs, si ≤ sj for all i

Definition 3: The complement of HFLTS Hs, is defined as

Hs = S - Hs ={ si / si S, si Hs }.

Definition 4: The envelope of the HFLTS env(Hs), is a linguistic interval whose

limits are obtained by means of upper bound (max) and lower bound (min). Hence

env(Hs)=[ Hs- ,Hs+]

Example2: Let S={ S0:nothing, S1 :very low, S2 :low, S3 :medium,

S4:high,S5:veryhigh,S6:perfect}be a linguistic term set, and Hs={ high,very

high,perfect } be an HFLTS of S, its envelope is

Hs- ={ high,very high,perfect }=high

Hs+ ={ high,very high,perfect }=perfect

env(Hs)=[ high , perfect] .

Document Classification for Large Datasets Based On Hesitant Fuzzy… 681

Table 1: Hesitant Fuzzy Linguistic Term Set (HFLTS)

Data

Set

S={ S0:nothing,

S1 :very low, S2 :low, S3:medium,

S4:high, S5:veryhigh, S6:perfect}

Hs+ ={ high, very

high, perfect

}=perfect

Hs- ={ high, very

high, perfect }=high

env(Hs)=[

high ,

perfect]

D1 {0,2,3,5,7,9,6} {7,9,6 }=6 {7,9,6 }=7 {7,6}

D2 {0,4,7,9,13,15,12} {13,15,12}=12 {13,15,12}=13 {13,12)

D3 {0,1,3,6,8,10,7} {8,10,7}=7 {8,10,7}=8 {8,7}

D4 {0,6,11,17,22,29,19} {22,29,19}=19 {22,29,19}=22 {22,19}

D5 {0,3,7,8,12,13,11 } {12,13,11}=11 {12,13,11}=12 {12,11}

D6 {0,9,24,29,35,40,33} {35,40,33}=33 {35,40,33}=35 {35,33}

D7 {0,7,11,16,22,27,21} {22,27,21 }=21 {22,27,21 }=22 {22,21}

D8 {0,5,9,14,17,23,16 } {17,23,16}=16 {17,23,16}=17 {17,16}

Table 2: Accuracy (in %) with Bag of Words Datasets ,20-news group Datasets and

Legal Case Reports Datasets

Bag of Word 20 News Group Le

gal

Case Report

No. of

Data Set

K-

NN

HFLTS Centroid SVM K-

NN

HFLTS Centroid SVM K-

NN

HFLTS Centroid SVM

50 0.84 0.97 0.87 0.89 0.83 0.93 0.87 0.80 0.81 0.91 0.82 0.85

100 0.86 0.94 0.86 0.71 0.82 0.94 0.83 0.71 0.82 0.92 0.83 0.76

200 0.82 0.92 0.85 0.73 0.81 0.96 0.85 0.83 0.82 0.93 0.84 0.85

350 0.80 0.93 0.79 0.76 0.90 0.91 0.73 0.86 0.90 0.91 0.78 0.84

500 0.77 0.89 0.73 0.78 0.84 0.89 0.73 0.78 0.83 0.89 0.78 0.78

650 0.78 0.88 0.76 0.79 0.75 0.83 0.75 0.79 0.72 0.82 0.78 0.74

800 0.73 0.86 0.72 0.72 0.73 0.96 0.72 0.82 0.73 0.92 0.77 0.82

1000 0.76 0.83 0.71 0.71 0.76 0.93 0.70 0.71 0.67 0.92 0.70 0.71

Table 3: F-measure value with Bag of Words datasets, 20-news group Datasets and

Legal Case Reports Datasets

Bag of Word 20 News Group Le

gal

Case Report

No. of

Data

Set

K-

NN

HFLTS Centroid SVM K-

NN

HFLTS Centroid SVM K-

NN

HFLTS Centroid SVM

5 0.82 0.97 0.86 0.88 0.81 0.92 0.86 0.88 0.81 0.96 0.86 0.84

10 0.83 0.94 0.87 0.72 0.84 0.94 0.77 0.77 0.84 0.95 0.85 0.72

20 0.82 0.92 0.84 0.73 0.82 0.92 0.84 0.73 0.83 0.96 0.84 0.76

35 0.83 0.93 0.80 0.72 0.82 0.93 0.70 0.77 0.86 0.93 0.86 0.72

50 0.87 0.89 0.74 0.78 0.87 0.92 0.74 0.78 0.87 0.88 0.74 0.75

682 Swatantra Kumar Sahu, Bharat Mishra and R.S. Thakur

65 0.88 0.92 0.77 0.72 0.88 0.92 0.77 0.77 0.88 0.98 0.75 0.72

80 0.83 0.86 0.71 0.72 0.82 0.96 0.71 0.72 0.84 0.88 0.71 0.75

100 0.56 0.83 0.72 0.74 0.56 0.93 0.72 0.74 0.56 0.84 0.75 0.74

3. METHODOLOGY:

In Classification of document, different steps are used. The steps are shown in fig 2.

Fig 2: Hesitant Fuzzy Linguistic Term Set

4 EXPERIMENTAL RESULTS

In this Experiment we calculate Hesitant Fuzzy Linguistic Term Set (HFLTS) in

Document dataset. Document Classification upper bound Hs+, envelope of the

HFLTS and lower bound Hs- of the HFLTS HS are calculated which describe in Table

1 and Table 2 respectively. Table 3 to Table 5 describes classification accuracy for

Bag of Words, 20-news group and Legal Case Reports Datasets respectively. Table 6

to Table 8 describes F-measure values for Bag of Words, 20-news group and Legal

Case Reports Datasets respectively.

This Experiment shows, Hesitant Fuzzy Linguistic Term Set (HFLTS) based

Document Classification is efficient and accurate compare to other Document

Classification. From Fig.2 to Fig. 9, Hesitant Fuzzy Linguistic Term Set is described.

Data

Collection

Data Preprocessing

Calculations of HFLTS

Calculations of Hs+ and Hs- Determine the envelope Classification Results

Document Classification for Large Datasets Based On Hesitant Fuzzy… 683

From Fig. 10 to Fig.11, Upper bound Hs+ , lower bound Hs- of the HFLTS are

described respectively.

Fig. 12 to Fig.14 describes classification accuracy results for Bag of Words, 20-news

group and Legal Case Reports Datasets respectively. Fig. 15 to Fig.17 describes F-

measure values for Bag of Words, 20-news group and Legal Case Reports Datasets

respectively.

D1H+ upper bound, D1H- lower bound are dataset 1, D2H+ upper bound, D2H- lower

bound are dataset 2, D3H+ upper bound, D3H- lower bound are dataset 3, D4H+ upper

bound, D4H- lower bound are dataset 4 , D5H+ upper bound, D5H- lower bound are

dataset 5, D6H+ upper bound, D6H- lower bound are Dataset 6, D7H+ upper bound,

D7H- lower bound are dataset 7, D8H+ upper bound, D8H- lower bound are dataset 8

in graphical representation of Fig.2 to Fig.9 respectively.

Fig 2: Hesitant Fuzzy Linguistic Term Set

Fig 3: Hesitant Fuzzy Linguistic Term Set

02468

10

Dat

a S

et 1

HFLTS

Data

05

101520

Dat

a S

et 2

HFLTS

Data

684 Swatantra Kumar Sahu, Bharat Mishra and R.S. Thakur

Fig 4: Hesitant Fuzzy Linguistic Term Set

Fig 5: Hesitant Fuzzy Linguistic Term Set

Fig 6: Hesitant Fuzzy Linguistic Term Set

02468

1012

Dat

a S

et 3

HFLTS

Data

05

101520253035

Dat

a S

et

4

HFLTS

Data

0

5

10

15

Dat

a S

et

5

HFLTS

Data

Document Classification for Large Datasets Based On Hesitant Fuzzy… 685

Fig 7: Hesitant Fuzzy Linguistic Term Set

Fig 8: Hesitant Fuzzy Linguistic Term Set

Fig 9: Hesitant Fuzzy Linguistic Term Set

0

10

20

30

40

50

Dat

a S

et

6

HFLTS

Data

0

5

10

15

20

25

30

Dat

a S

et 7

HFLTS

Data

05

10152025

Dat

a S

et 8

HFLTS

Data

686 Swatantra Kumar Sahu, Bharat Mishra and R.S. Thakur

Fig 10: Hesitant Fuzzy Linguistic Term Set

Fig 11: Hesitant Fuzzy Linguistic Term Set

Fig 12: Accuracy for Bag of Words datasets

0

5

10

15

20

25

Dat

a S

et 1

,2,3

,4

HFLTS

Data

0

5

10

15

20

25

30

35

40

Dat

a S

et 5

,6,7

,8

HFLTS

Data

0

0.2

0.4

0.6

0.8

1

1.2

50 100 200 350 500 650 800 1000

Acc

ura

cy %

Number of Clusters

Bag of Words Datasets

K-NN

HFLTS

centroid

SVM

Document Classification for Large Datasets Based On Hesitant Fuzzy… 687

Fig 13: Accuracy for 20-news group datasets

Fig 14: Accuracy for Legal Case Reports Datasets

Fig 15: F-measure for Bag of Words datasets

0

0.5

1

1.5

20

-ne

ws

gro

up

Dat

ase

ts f

or

Acc

ura

cy %

Number of Clusters

20-news group Datasets

K-NN

HFLTS

centroid

SVM

0

0.5

1

1.5

Lega

l Cas

e R

ep

ort

s D

atas

ets

fo

r A

ccu

racy

%

Number of Clusters

Legal Case Reports Datasets

K-NN

HFLTS

Centroid

SVM

0

0.2

0.4

0.6

0.8

1

1.2

5 10 20 35 50 65 80 100Over

all

F-m

easu

re

Number of Clusters

Bag of Words Datasets

K-NN

HFLTS

Centroid

SVM

688 Swatantra Kumar Sahu, Bharat Mishra and R.S. Thakur

Fig 16: F-measure from 20-news group Datasets

Fig 17: F-measure from Legal Case Reports Datasets

5. CONCLUSION:

As result & analysis shows that The Document Classification based on Hesitant Fuzzy

Linguistic Term Set is efficient and the HFLTS classification has the potential to

improve the classification accuracy.

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